After playing this difficulty there are only a few things you need to be aware of compared to standard difficulties:
1. Back-up your save data on either a USB memory stick or Cloud storage (remember if using cloud storage, disable it during playing or it will sync to your hard-drive save. This invalidates your save data if you die).
2. Watch out for instant-kill areas and quick time events (QTE's). Although the QTE's are easily done don't get distracted when they're nearby. Some areas may slip you up if you rush such as chapter 14's gassing rooms, 16's spinning fan blade, and especially the falling rocks/stasis areas when scalling the icy mountains in chapter 13.
3. Play the other new game+ modes first as you'll get a good feel for the levels and enemy spawns. You also get packs of equipment etc for completing modes like Pure Survival or collecting the collectables.
4. Skip all optional missions as they'll only slow you down.
5. Stick to one weapon (plasma cutter, evangelizer or something similair) and keep upgrading it.
6. Upgrade your armour and health as soon as you can.
7. Take regular save breaks for your USB (I did it from Chapter 8 the beggining to the arrival at Tau Volantis, Chapter 14 and then the beggining of Chapter 19 (in-case the flying objects of death hit me). You can save more than this if you're not very confident you'll do everything fine.
8. Sell unused weapon parts (i.e. attatchments, upgrade circuits & handles). You'll want the extra resources.
9. The enemies known as 'Feeders' (starved looking agile ones) are a pain as they usually attack in large groups. Later in the game they also become a dark shade of black with red eyes and are very difficult to kill as they cannot be dismembered. Headshots work wonders, but if you only use 1 gun in the game you might consider also buying a contact beam for your second gun as its secondary fire mode which shoots the ground. This when upgraded with damage and fire rate is great for feeder swarms.
10. Learn to use the combat roll effectively. By double tapping the LB you'll perform a combat roll. When rolling, 9 times out of 10 you'll negate any damage so it's very useful if a necromorph has the jump on you and is about to attack. You can also chain rolls for certain scenarios such as dodging bullets from Danik's gunships, or simply distancing yourself from a swarm of necromorphs.
11. Save up your ration seals till you get 60, always sending your bots out to get resources from resource spots (you'll hear a noise chime). You can then go to a bench, select downloadable content (Y button) and buy an Epic weapon & resource pack with the seals (X button).
1x Epic pack contains:
2000 scrap metal
400 somatic gel
2x Weapon parts
NOTE: People have mentioned in many ways how it is more efficient to buy the smaller packs. If you REALLY want to get lots of resources you can instead buy smaller packs to have earlier access to upgrades etc. However it is by no means essential for this difficulty.
Lastly remember to back-up your saves (which I highly reccomend). Even if like me you don't actually die during this difficulty mode, if you don't back-up your saves you could get killed by a jammy enemy or QTE.
(V Sully posted a great tip for a useful weapon in the comments):